\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{16}   &  2.0 & +  4.00 x_{1} & +  6.00 x_{2} & +  1.00 x_{3} & -9.00 x_{4} & +  1.00 x_{5} & + 10.00 x_{6} & +  6.00 x_{7} & -8.00 x_{8} & + 10.00 x_{9} & +  6.00 x_{10} & -6.00 x_{11} & +  6.00 x_{12} & -7.00 x_{13} & +  3.00 x_{14} & +  3.00 x_{15}\\
 x_{17}   &  3.0 & +  4.00 x_{1} & +  4.00 x_{2} & -2.00 x_{3} &   & -5.00 x_{5} & -4.00 x_{6} & +  6.00 x_{7} & -9.00 x_{8} & -6.00 x_{9} & -4.00 x_{10} & -1.00 x_{11} & -9.00 x_{12} & -9.00 x_{13} & -9.00 x_{14} & +  5.00 x_{15}\\
 x_{18}   &  -1.0 & +  6.00 x_{1} & +  1.00 x_{2} & +  8.00 x_{3} & -6.00 x_{4} & +  4.00 x_{5} & +  8.00 x_{6} & -1.00 x_{7} & +  3.00 x_{8} & -5.00 x_{9} & -8.00 x_{10} & +  1.00 x_{11} & +  6.00 x_{12} & +  1.00 x_{13} & + 10.00 x_{14} & +  6.00 x_{15}\\
 x_{19}   &  3.0 & +  3.00 x_{1} & -8.00 x_{2} & +  6.00 x_{3} &   & -4.00 x_{5} & -6.00 x_{6} & -2.00 x_{7} & -7.00 x_{8} & +  9.00 x_{9} & + 10.00 x_{10} & -5.00 x_{11} & -4.00 x_{12} & +  8.00 x_{13} & +  5.00 x_{14} &   \\
 x_{20}   &  1.0 & +  9.00 x_{1} & -3.00 x_{2} &   & -2.00 x_{4} & + 10.00 x_{5} & -6.00 x_{6} & -7.00 x_{7} & +  6.00 x_{8} & +  6.00 x_{9} & +  5.00 x_{10} & -1.00 x_{11} & +  9.00 x_{12} &   & -7.00 x_{14} & -1.00 x_{15}\\
 x_{21}   &  2.0 & -1.00 x_{1} & +  8.00 x_{2} & +  7.00 x_{3} & -1.00 x_{4} & -1.00 x_{5} & -5.00 x_{6} & -1.00 x_{7} & -5.00 x_{8} & +  6.00 x_{9} & +  1.00 x_{10} & -5.00 x_{11} & +  2.00 x_{12} & +  3.00 x_{13} & + 10.00 x_{14} & + 10.00 x_{15}\\
 x_{22}   &  -1.0 & -5.00 x_{1} & +  5.00 x_{2} & -10.00 x_{3} &   & +  5.00 x_{5} & +  2.00 x_{6} & -9.00 x_{7} & + 10.00 x_{8} & +  4.00 x_{9} & + 10.00 x_{10} & -5.00 x_{11} &   & +  2.00 x_{13} & -4.00 x_{14} & +  4.00 x_{15}\\
 x_{23}   &  -2.0 & -2.00 x_{1} & +  8.00 x_{2} & +  7.00 x_{3} & -7.00 x_{4} & -5.00 x_{5} & +  4.00 x_{6} & -7.00 x_{7} & -10.00 x_{8} & +  3.00 x_{9} &   & +  8.00 x_{11} &   & +  6.00 x_{13} & -6.00 x_{14} & +  1.00 x_{15}\\
 x_{24}   &  0.0 & -2.00 x_{1} & +  5.00 x_{2} & +  3.00 x_{3} & +  3.00 x_{4} & -4.00 x_{5} & -4.00 x_{6} & +  1.00 x_{7} & -9.00 x_{8} & +  4.00 x_{9} & -10.00 x_{10} & +  8.00 x_{11} & +  4.00 x_{12} & +  3.00 x_{13} & -8.00 x_{14} & -8.00 x_{15}\\
 x_{25}   &  3.0 & -1.00 x_{1} & +  4.00 x_{2} & + 10.00 x_{3} & -10.00 x_{4} & +  7.00 x_{5} & +  6.00 x_{6} &   & -2.00 x_{8} & -10.00 x_{9} &   & -1.00 x_{11} & -9.00 x_{12} & +  5.00 x_{13} & +  2.00 x_{14} & -2.00 x_{15}\\
 x_{26}   &  2.0 & -10.00 x_{1} & +  5.00 x_{2} & +  5.00 x_{3} & -7.00 x_{4} & -8.00 x_{5} & -8.00 x_{6} & -8.00 x_{7} & + 10.00 x_{8} &   & +  1.00 x_{10} & -10.00 x_{11} & -7.00 x_{12} & +  6.00 x_{13} & +  4.00 x_{14} & +  3.00 x_{15}\\
 x_{27}   &  -1.0 & +  2.00 x_{1} & -7.00 x_{2} & +  3.00 x_{3} &   & -3.00 x_{5} & +  7.00 x_{6} & +  8.00 x_{7} & +  4.00 x_{8} & +  1.00 x_{9} & +  4.00 x_{10} & +  6.00 x_{11} & +  7.00 x_{12} & +  1.00 x_{13} & -3.00 x_{14} & +  1.00 x_{15}\\
 x_{28}   &  3.0 & -5.00 x_{1} & +  9.00 x_{2} & +  5.00 x_{3} & -2.00 x_{4} & +  8.00 x_{5} & +  6.00 x_{6} & -8.00 x_{7} & +  9.00 x_{8} & -9.00 x_{9} & +  6.00 x_{10} & +  2.00 x_{11} & -3.00 x_{12} & +  8.00 x_{13} & -4.00 x_{14} & +  5.00 x_{15}\\
 x_{29}   &  -1.0 & +  6.00 x_{1} & -4.00 x_{2} & -10.00 x_{3} & -6.00 x_{4} & -6.00 x_{5} & -8.00 x_{6} & +  4.00 x_{7} & +  3.00 x_{8} & -2.00 x_{9} & +  9.00 x_{10} & -6.00 x_{11} & +  9.00 x_{12} & -2.00 x_{13} & -4.00 x_{14} & -3.00 x_{15}\\
 x_{30}   &  -1.0 & +  1.00 x_{1} & +  3.00 x_{2} & +  9.00 x_{3} & + 10.00 x_{4} & -6.00 x_{5} & -10.00 x_{6} & +  4.00 x_{7} & +  8.00 x_{8} & +  7.00 x_{9} & -2.00 x_{10} & -9.00 x_{11} & +  7.00 x_{12} & -5.00 x_{13} &   & -9.00 x_{15}\\
 x_{31}   &  -3.0 & +  3.00 x_{1} & -8.00 x_{2} & +  9.00 x_{3} & -9.00 x_{4} & -5.00 x_{5} & -5.00 x_{6} & +  8.00 x_{7} & -9.00 x_{8} & + 10.00 x_{9} & -6.00 x_{10} & +  3.00 x_{11} & -2.00 x_{12} &   & +  5.00 x_{14} & +  3.00 x_{15}\\
 x_{32}   &  -1.0 & -3.00 x_{1} & +  5.00 x_{2} & +  6.00 x_{3} & +  6.00 x_{4} & -9.00 x_{5} & -9.00 x_{6} & -1.00 x_{7} & -10.00 x_{8} & -5.00 x_{9} & +  2.00 x_{10} & +  3.00 x_{11} & +  3.00 x_{12} & +  2.00 x_{13} & +  9.00 x_{14} & +  9.00 x_{15}\\
 x_{33}   &  0.0 & -3.00 x_{1} & +  8.00 x_{2} & +  1.00 x_{3} & -1.00 x_{4} & -6.00 x_{5} & -3.00 x_{6} & -2.00 x_{7} & -2.00 x_{8} & +  3.00 x_{9} & +  1.00 x_{10} & +  8.00 x_{11} & -8.00 x_{12} & +  2.00 x_{13} & -6.00 x_{14} & +  1.00 x_{15}\\
 x_{34}   &  -3.0 & -2.00 x_{1} & + 10.00 x_{2} & +  9.00 x_{3} & -9.00 x_{4} & +  3.00 x_{5} & +  6.00 x_{6} & -7.00 x_{7} & -8.00 x_{8} & +  8.00 x_{9} & -8.00 x_{10} & +  1.00 x_{11} & +  3.00 x_{12} & -6.00 x_{13} & + 10.00 x_{14} & -7.00 x_{15}\\
\hline
z    &  0.0 & -2.00 x_{1} & -5.00 x_{2} & -2.00 x_{3} & +  4.00 x_{4} & +  3.00 x_{5} & -3.00 x_{6} & +  2.00 x_{7} & -5.00 x_{8} & -3.00 x_{9} & +  2.00 x_{10} & -3.00 x_{11} & -1.00 x_{12} & -5.00 x_{13} & -2.00 x_{14} & -4.00 x_{15}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{15}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,34$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -4.00 y_{16} & -4.00 y_{17} & -6.00 y_{18} & -3.00 y_{19} & -9.00 y_{20} & +  1.00 y_{21} & +  5.00 y_{22} & +  2.00 y_{23} & +  2.00 y_{24} & +  1.00 y_{25} & + 10.00 y_{26} & -2.00 y_{27} & +  5.00 y_{28} & -6.00 y_{29} & -1.00 y_{30} & -3.00 y_{31} & +  3.00 y_{32} & +  3.00 y_{33} & +  2.00 y_{34}\\
 y_{2}   &  1.0 & -6.00 y_{16} & -4.00 y_{17} & -1.00 y_{18} & +  8.00 y_{19} & +  3.00 y_{20} & -8.00 y_{21} & -5.00 y_{22} & -8.00 y_{23} & -5.00 y_{24} & -4.00 y_{25} & -5.00 y_{26} & +  7.00 y_{27} & -9.00 y_{28} & +  4.00 y_{29} & -3.00 y_{30} & +  8.00 y_{31} & -5.00 y_{32} & -8.00 y_{33} & -10.00 y_{34}\\
 y_{3}   &  1.0 & -1.00 y_{16} & +  2.00 y_{17} & -8.00 y_{18} & -6.00 y_{19} &   & -7.00 y_{21} & + 10.00 y_{22} & -7.00 y_{23} & -3.00 y_{24} & -10.00 y_{25} & -5.00 y_{26} & -3.00 y_{27} & -5.00 y_{28} & + 10.00 y_{29} & -9.00 y_{30} & -9.00 y_{31} & -6.00 y_{32} & -1.00 y_{33} & -9.00 y_{34}\\
 y_{4}   &  1.0 & +  9.00 y_{16} &   & +  6.00 y_{18} &   & +  2.00 y_{20} & +  1.00 y_{21} &   & +  7.00 y_{23} & -3.00 y_{24} & + 10.00 y_{25} & +  7.00 y_{26} &   & +  2.00 y_{28} & +  6.00 y_{29} & -10.00 y_{30} & +  9.00 y_{31} & -6.00 y_{32} & +  1.00 y_{33} & +  9.00 y_{34}\\
 y_{5}   &  1.0 & -1.00 y_{16} & +  5.00 y_{17} & -4.00 y_{18} & +  4.00 y_{19} & -10.00 y_{20} & +  1.00 y_{21} & -5.00 y_{22} & +  5.00 y_{23} & +  4.00 y_{24} & -7.00 y_{25} & +  8.00 y_{26} & +  3.00 y_{27} & -8.00 y_{28} & +  6.00 y_{29} & +  6.00 y_{30} & +  5.00 y_{31} & +  9.00 y_{32} & +  6.00 y_{33} & -3.00 y_{34}\\
 y_{6}   &  1.0 & -10.00 y_{16} & +  4.00 y_{17} & -8.00 y_{18} & +  6.00 y_{19} & +  6.00 y_{20} & +  5.00 y_{21} & -2.00 y_{22} & -4.00 y_{23} & +  4.00 y_{24} & -6.00 y_{25} & +  8.00 y_{26} & -7.00 y_{27} & -6.00 y_{28} & +  8.00 y_{29} & + 10.00 y_{30} & +  5.00 y_{31} & +  9.00 y_{32} & +  3.00 y_{33} & -6.00 y_{34}\\
 y_{7}   &  1.0 & -6.00 y_{16} & -6.00 y_{17} & +  1.00 y_{18} & +  2.00 y_{19} & +  7.00 y_{20} & +  1.00 y_{21} & +  9.00 y_{22} & +  7.00 y_{23} & -1.00 y_{24} &   & +  8.00 y_{26} & -8.00 y_{27} & +  8.00 y_{28} & -4.00 y_{29} & -4.00 y_{30} & -8.00 y_{31} & +  1.00 y_{32} & +  2.00 y_{33} & +  7.00 y_{34}\\
 y_{8}   &  1.0 & +  8.00 y_{16} & +  9.00 y_{17} & -3.00 y_{18} & +  7.00 y_{19} & -6.00 y_{20} & +  5.00 y_{21} & -10.00 y_{22} & + 10.00 y_{23} & +  9.00 y_{24} & +  2.00 y_{25} & -10.00 y_{26} & -4.00 y_{27} & -9.00 y_{28} & -3.00 y_{29} & -8.00 y_{30} & +  9.00 y_{31} & + 10.00 y_{32} & +  2.00 y_{33} & +  8.00 y_{34}\\
 y_{9}   &  1.0 & -10.00 y_{16} & +  6.00 y_{17} & +  5.00 y_{18} & -9.00 y_{19} & -6.00 y_{20} & -6.00 y_{21} & -4.00 y_{22} & -3.00 y_{23} & -4.00 y_{24} & + 10.00 y_{25} &   & -1.00 y_{27} & +  9.00 y_{28} & +  2.00 y_{29} & -7.00 y_{30} & -10.00 y_{31} & +  5.00 y_{32} & -3.00 y_{33} & -8.00 y_{34}\\
 y_{10}   &  1.0 & -6.00 y_{16} & +  4.00 y_{17} & +  8.00 y_{18} & -10.00 y_{19} & -5.00 y_{20} & -1.00 y_{21} & -10.00 y_{22} &   & + 10.00 y_{24} &   & -1.00 y_{26} & -4.00 y_{27} & -6.00 y_{28} & -9.00 y_{29} & +  2.00 y_{30} & +  6.00 y_{31} & -2.00 y_{32} & -1.00 y_{33} & +  8.00 y_{34}\\
 y_{11}   &  1.0 & +  6.00 y_{16} & +  1.00 y_{17} & -1.00 y_{18} & +  5.00 y_{19} & +  1.00 y_{20} & +  5.00 y_{21} & +  5.00 y_{22} & -8.00 y_{23} & -8.00 y_{24} & +  1.00 y_{25} & + 10.00 y_{26} & -6.00 y_{27} & -2.00 y_{28} & +  6.00 y_{29} & +  9.00 y_{30} & -3.00 y_{31} & -3.00 y_{32} & -8.00 y_{33} & -1.00 y_{34}\\
 y_{12}   &  1.0 & -6.00 y_{16} & +  9.00 y_{17} & -6.00 y_{18} & +  4.00 y_{19} & -9.00 y_{20} & -2.00 y_{21} &    &   & -4.00 y_{24} & +  9.00 y_{25} & +  7.00 y_{26} & -7.00 y_{27} & +  3.00 y_{28} & -9.00 y_{29} & -7.00 y_{30} & +  2.00 y_{31} & -3.00 y_{32} & +  8.00 y_{33} & -3.00 y_{34}\\
 y_{13}   &  1.0 & +  7.00 y_{16} & +  9.00 y_{17} & -1.00 y_{18} & -8.00 y_{19} &   & -3.00 y_{21} & -2.00 y_{22} & -6.00 y_{23} & -3.00 y_{24} & -5.00 y_{25} & -6.00 y_{26} & -1.00 y_{27} & -8.00 y_{28} & +  2.00 y_{29} & +  5.00 y_{30} &   & -2.00 y_{32} & -2.00 y_{33} & +  6.00 y_{34}\\
 y_{14}   &  1.0 & -3.00 y_{16} & +  9.00 y_{17} & -10.00 y_{18} & -5.00 y_{19} & +  7.00 y_{20} & -10.00 y_{21} & +  4.00 y_{22} & +  6.00 y_{23} & +  8.00 y_{24} & -2.00 y_{25} & -4.00 y_{26} & +  3.00 y_{27} & +  4.00 y_{28} & +  4.00 y_{29} &   & -5.00 y_{31} & -9.00 y_{32} & +  6.00 y_{33} & -10.00 y_{34}\\
 y_{15}   &  1.0 & -3.00 y_{16} & -5.00 y_{17} & -6.00 y_{18} &   & +  1.00 y_{20} & -10.00 y_{21} & -4.00 y_{22} & -1.00 y_{23} & +  8.00 y_{24} & +  2.00 y_{25} & -3.00 y_{26} & -1.00 y_{27} & -5.00 y_{28} & +  3.00 y_{29} & +  9.00 y_{30} & -3.00 y_{31} & -9.00 y_{32} & -1.00 y_{33} & +  7.00 y_{34}\\
\hline
z    &  -0 & -2.00 y_{16} & -3.00 y_{17} & +  1.00 y_{18} & -3.00 y_{19} & -1.00 y_{20} & -2.00 y_{21} & +  1.00 y_{22} & +  2.00 y_{23} &   & -3.00 y_{25} & -2.00 y_{26} & +  1.00 y_{27} & -3.00 y_{28} & +  1.00 y_{29} & +  1.00 y_{30} & +  3.00 y_{31} & +  1.00 y_{32} &   & +  3.00 y_{34}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 35 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{33}   &  0.200884182553 & +  0.08 y_{16} & +  0.01 y_{15} & -0.01 y_{9} & -0.52 y_{19} & -0.10 y_{11} & +  0.44 y_{21} & +  1.00 y_{30} & -0.41 y_{27} & -1.09 y_{20} & -0.05 y_{10} & +  1.33 y_{26} & +  0.03 y_{12} & -0.40 y_{28} & -0.13 y_{24} & -0.01 y_{2} & -0.09 y_{1} & -0.00 y_{3} & -1.02 y_{23} & +  0.04 y_{7}\\
 y_{13}   &  1.02238978196 & -5.53 y_{16} & +  0.02 y_{15} & -0.21 y_{9} & +  9.98 y_{19} & +  0.66 y_{11} & -10.17 y_{21} & -8.50 y_{30} & +  3.62 y_{27} & + 14.61 y_{20} & +  0.80 y_{10} & -7.81 y_{26} & -0.30 y_{12} & +  1.87 y_{28} & -13.02 y_{24} & -0.89 y_{2} & +  0.52 y_{1} & +  0.50 y_{3} & +  1.93 y_{23} & -1.13 y_{7}\\
 y_{8}   &  3.65385877907 & -17.57 y_{16} & -0.10 y_{15} & -0.27 y_{9} & + 27.54 y_{19} & +  0.59 y_{11} & -13.77 y_{21} & -34.91 y_{30} & -11.91 y_{27} & + 24.59 y_{20} & +  0.38 y_{10} & -15.62 y_{26} & -0.64 y_{12} & -3.53 y_{28} & -6.69 y_{24} & -1.41 y_{2} & +  1.62 y_{1} & -0.29 y_{3} & + 15.07 y_{23} & -2.54 y_{7}\\
 y_{4}   &  4.36346831316 & -10.74 y_{16} & +  0.28 y_{15} & -0.71 y_{9} & -37.19 y_{19} & +  0.54 y_{11} & -11.01 y_{21} & -25.78 y_{30} & +  2.28 y_{27} & -29.39 y_{20} & -1.13 y_{10} & +  7.94 y_{26} & +  0.67 y_{12} & +  0.41 y_{28} & + 11.42 y_{24} & -0.20 y_{2} & -2.43 y_{1} & -1.15 y_{3} & -0.75 y_{23} & +  0.77 y_{7}\\
 y_{5}   &  5.01177601889 & -21.28 y_{16} & -0.22 y_{15} & -0.24 y_{9} & + 20.01 y_{19} & -0.54 y_{11} & -6.94 y_{21} & -1.43 y_{30} & -13.06 y_{27} & +  4.45 y_{20} & -0.27 y_{10} & + 21.95 y_{26} & -0.70 y_{12} & -3.63 y_{28} & -7.44 y_{24} & -1.01 y_{2} & +  0.69 y_{1} & +  0.21 y_{3} & +  5.23 y_{23} & -1.93 y_{7}\\
 y_{22}   &  0.0151790513764 & -0.55 y_{16} & -0.04 y_{15} & -0.03 y_{9} & -1.32 y_{19} & +  0.05 y_{11} & -0.89 y_{21} & +  0.04 y_{30} & +  0.64 y_{27} & -0.86 y_{20} & -0.03 y_{10} & -0.96 y_{26} & +  0.03 y_{12} & -0.36 y_{28} & +  1.13 y_{24} & +  0.00 y_{2} & -0.04 y_{1} & -0.01 y_{3} & -0.12 y_{23} & +  0.06 y_{7}\\
 y_{17}   &  0.00123970777898 & -0.74 y_{16} & -0.02 y_{15} & -0.00 y_{9} & +  0.88 y_{19} & +  0.05 y_{11} & -0.63 y_{21} & -0.45 y_{30} & +  0.49 y_{27} & +  1.01 y_{20} & +  0.04 y_{10} & -0.37 y_{26} & +  0.01 y_{12} & +  0.34 y_{28} & -0.10 y_{24} & -0.06 y_{2} & +  0.02 y_{1} & +  0.03 y_{3} & +  0.55 y_{23} & -0.07 y_{7}\\
 y_{14}   &  0.0598837047658 & +  2.50 y_{16} & +  0.20 y_{15} & +  0.04 y_{9} & -2.13 y_{19} & -0.32 y_{11} & +  1.50 y_{21} & + 13.36 y_{30} & +  7.42 y_{27} & + 10.62 y_{20} & -0.05 y_{10} & +  3.49 y_{26} & +  0.71 y_{12} & +  8.27 y_{28} & + 10.55 y_{24} & -0.02 y_{2} & -0.39 y_{1} & +  0.86 y_{3} & + 10.95 y_{23} & -0.08 y_{7}\\
 y_{31}   &  0.149490626712 & -1.06 y_{16} & -0.02 y_{15} & -0.05 y_{9} & -1.38 y_{19} & +  0.03 y_{11} & -0.86 y_{21} & -0.63 y_{30} & -0.30 y_{27} & -0.52 y_{20} & -0.03 y_{10} & -0.21 y_{26} & +  0.02 y_{12} & +  0.28 y_{28} & +  0.58 y_{24} & +  0.01 y_{2} & -0.03 y_{1} & -0.04 y_{3} & -0.02 y_{23} & -0.02 y_{7}\\
 y_{18}   &  0.0517741514442 & +  0.48 y_{16} & -0.03 y_{15} & +  0.01 y_{9} & -0.76 y_{19} & -0.03 y_{11} & +  0.11 y_{21} & +  0.92 y_{30} & +  0.19 y_{27} & -1.70 y_{20} & -0.01 y_{10} & +  0.64 y_{26} & +  0.01 y_{12} & -0.33 y_{28} & +  0.54 y_{24} & +  0.03 y_{2} & -0.12 y_{1} & -0.01 y_{3} & -0.58 y_{23} & +  0.10 y_{7}\\
 y_{34}   &  0.0662920835459 & -1.02 y_{16} & +  0.02 y_{15} & -0.03 y_{9} & +  0.33 y_{19} & +  0.04 y_{11} & -0.75 y_{21} & -1.35 y_{30} & +  0.26 y_{27} & +  0.23 y_{20} & +  0.02 y_{10} & -0.41 y_{26} & -0.02 y_{12} & +  0.18 y_{28} & -0.59 y_{24} & -0.06 y_{2} & +  0.02 y_{1} & -0.01 y_{3} & -0.08 y_{23} & -0.04 y_{7}\\
 y_{29}   &  0.24678990481 & -1.37 y_{16} & +  0.02 y_{15} & -0.02 y_{9} & -0.68 y_{19} & +  0.00 y_{11} & -0.38 y_{21} & -0.79 y_{30} & -0.56 y_{27} & -0.93 y_{20} & -0.07 y_{10} & +  0.80 y_{26} & -0.02 y_{12} & +  0.06 y_{28} & +  0.23 y_{24} & -0.04 y_{2} & -0.07 y_{1} & -0.02 y_{3} & -0.11 y_{23} & -0.03 y_{7}\\
 y_{25}   &  0.0247101295877 & -0.13 y_{16} & +  0.02 y_{15} & +  0.01 y_{9} & -1.34 y_{19} & +  0.03 y_{11} & -0.21 y_{21} & -0.38 y_{30} & +  0.16 y_{27} & -0.53 y_{20} & -0.05 y_{10} & -0.59 y_{26} & +  0.04 y_{12} & -0.60 y_{28} & +  0.82 y_{24} & +  0.01 y_{2} & -0.04 y_{1} & -0.06 y_{3} & -0.16 y_{23} & +  0.03 y_{7}\\
 y_{6}   &  4.56573800038 & -33.18 y_{16} & -0.25 y_{15} & -0.26 y_{9} & + 18.06 y_{19} & -0.11 y_{11} & -5.48 y_{21} & -1.41 y_{30} & -22.91 y_{27} & + 23.82 y_{20} & -0.45 y_{10} & + 15.13 y_{26} & -0.68 y_{12} & -1.54 y_{28} & -2.66 y_{24} & -0.90 y_{2} & +  1.08 y_{1} & +  0.14 y_{3} & +  0.56 y_{23} & -2.13 y_{7}\\
 y_{32}   &  0.136324315852 & -0.93 y_{16} & -0.03 y_{15} & +  0.01 y_{9} & +  0.86 y_{19} & +  0.01 y_{11} & -0.95 y_{21} & -0.68 y_{30} & -0.60 y_{27} & +  1.11 y_{20} & -0.01 y_{10} & -0.39 y_{26} & -0.05 y_{12} & -0.39 y_{28} & -0.30 y_{24} & -0.05 y_{2} & +  0.09 y_{1} & -0.02 y_{3} & +  0.00 y_{23} & -0.09 y_{7}\\
\hline
z    &  1.01956604216 & -8.01 y_{16} & -0.07 y_{15} & -0.28 y_{9} & -6.66 y_{19} & -0.01 y_{11} & -6.40 y_{21} & -2.96 y_{30} & -1.42 y_{27} & -5.65 y_{20} & -0.13 y_{10} & -0.91 y_{26} & -0.19 y_{12} & -1.85 y_{28} & -0.59 y_{24} & -0.08 y_{2} & -0.11 y_{1} & -0.14 y_{3} & -0.28 y_{23} & -0.01 y_{7}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{16}   &  8.00864603917 & -0.08 x_{33} & +  5.53 x_{13} & + 17.57 x_{8} & + 10.74 x_{4} & + 21.28 x_{5} & +  0.55 x_{22} & +  0.74 x_{17} & -2.50 x_{14} & +  1.06 x_{31} & -0.48 x_{18} & +  1.02 x_{34} & +  1.37 x_{29} & +  0.13 x_{25} & + 33.18 x_{6} & +  0.93 x_{32}\\
 x_{15}   &  0.0745432908887 & -0.01 x_{33} & -0.02 x_{13} & +  0.10 x_{8} & -0.28 x_{4} & +  0.22 x_{5} & +  0.04 x_{22} & +  0.02 x_{17} & -0.20 x_{14} & +  0.02 x_{31} & +  0.03 x_{18} & -0.02 x_{34} & -0.02 x_{29} & -0.02 x_{25} & +  0.25 x_{6} & +  0.03 x_{32}\\
 x_{9}   &  0.281173975013 & +  0.01 x_{33} & +  0.21 x_{13} & +  0.27 x_{8} & +  0.71 x_{4} & +  0.24 x_{5} & +  0.03 x_{22} & +  0.00 x_{17} & -0.04 x_{14} & +  0.05 x_{31} & -0.01 x_{18} & +  0.03 x_{34} & +  0.02 x_{29} & -0.01 x_{25} & +  0.26 x_{6} & -0.01 x_{32}\\
 x_{19}   &  6.66236932572 & +  0.52 x_{33} & -9.98 x_{13} & -27.54 x_{8} & + 37.19 x_{4} & -20.01 x_{5} & +  1.32 x_{22} & -0.88 x_{17} & +  2.13 x_{14} & +  1.38 x_{31} & +  0.76 x_{18} & -0.33 x_{34} & +  0.68 x_{29} & +  1.34 x_{25} & -18.06 x_{6} & -0.86 x_{32}\\
 x_{11}   &  0.00523102270954 & +  0.10 x_{33} & -0.66 x_{13} & -0.59 x_{8} & -0.54 x_{4} & +  0.54 x_{5} & -0.05 x_{22} & -0.05 x_{17} & +  0.32 x_{14} & -0.03 x_{31} & +  0.03 x_{18} & -0.04 x_{34} & -0.00 x_{29} & -0.03 x_{25} & +  0.11 x_{6} & -0.01 x_{32}\\
 x_{21}   &  6.40272113021 & -0.44 x_{33} & + 10.17 x_{13} & + 13.77 x_{8} & + 11.01 x_{4} & +  6.94 x_{5} & +  0.89 x_{22} & +  0.63 x_{17} & -1.50 x_{14} & +  0.86 x_{31} & -0.11 x_{18} & +  0.75 x_{34} & +  0.38 x_{29} & +  0.21 x_{25} & +  5.48 x_{6} & +  0.95 x_{32}\\
 x_{30}   &  2.96272483932 & -1.00 x_{33} & +  8.50 x_{13} & + 34.91 x_{8} & + 25.78 x_{4} & +  1.43 x_{5} & -0.04 x_{22} & +  0.45 x_{17} & -13.36 x_{14} & +  0.63 x_{31} & -0.92 x_{18} & +  1.35 x_{34} & +  0.79 x_{29} & +  0.38 x_{25} & +  1.41 x_{6} & +  0.68 x_{32}\\
 x_{27}   &  1.41904428752 & +  0.41 x_{33} & -3.62 x_{13} & + 11.91 x_{8} & -2.28 x_{4} & + 13.06 x_{5} & -0.64 x_{22} & -0.49 x_{17} & -7.42 x_{14} & +  0.30 x_{31} & -0.19 x_{18} & -0.26 x_{34} & +  0.56 x_{29} & -0.16 x_{25} & + 22.91 x_{6} & +  0.60 x_{32}\\
 x_{20}   &  5.65104462738 & +  1.09 x_{33} & -14.61 x_{13} & -24.59 x_{8} & + 29.39 x_{4} & -4.45 x_{5} & +  0.86 x_{22} & -1.01 x_{17} & -10.62 x_{14} & +  0.52 x_{31} & +  1.70 x_{18} & -0.23 x_{34} & +  0.93 x_{29} & +  0.53 x_{25} & -23.82 x_{6} & -1.11 x_{32}\\
 x_{10}   &  0.13177966004 & +  0.05 x_{33} & -0.80 x_{13} & -0.38 x_{8} & +  1.13 x_{4} & +  0.27 x_{5} & +  0.03 x_{22} & -0.04 x_{17} & +  0.05 x_{14} & +  0.03 x_{31} & +  0.01 x_{18} & -0.02 x_{34} & +  0.07 x_{29} & +  0.05 x_{25} & +  0.45 x_{6} & +  0.01 x_{32}\\
 x_{26}   &  0.909412281081 & -1.33 x_{33} & +  7.81 x_{13} & + 15.62 x_{8} & -7.94 x_{4} & -21.95 x_{5} & +  0.96 x_{22} & +  0.37 x_{17} & -3.49 x_{14} & +  0.21 x_{31} & -0.64 x_{18} & +  0.41 x_{34} & -0.80 x_{29} & +  0.59 x_{25} & -15.13 x_{6} & +  0.39 x_{32}\\
 x_{12}   &  0.185517894132 & -0.03 x_{33} & +  0.30 x_{13} & +  0.64 x_{8} & -0.67 x_{4} & +  0.70 x_{5} & -0.03 x_{22} & -0.01 x_{17} & -0.71 x_{14} & -0.02 x_{31} & -0.01 x_{18} & +  0.02 x_{34} & +  0.02 x_{29} & -0.04 x_{25} & +  0.68 x_{6} & +  0.05 x_{32}\\
 x_{28}   &  1.85251730507 & +  0.40 x_{33} & -1.87 x_{13} & +  3.53 x_{8} & -0.41 x_{4} & +  3.63 x_{5} & +  0.36 x_{22} & -0.34 x_{17} & -8.27 x_{14} & -0.28 x_{31} & +  0.33 x_{18} & -0.18 x_{34} & -0.06 x_{29} & +  0.60 x_{25} & +  1.54 x_{6} & +  0.39 x_{32}\\
 x_{24}   &  0.59054637452 & +  0.13 x_{33} & + 13.02 x_{13} & +  6.69 x_{8} & -11.42 x_{4} & +  7.44 x_{5} & -1.13 x_{22} & +  0.10 x_{17} & -10.55 x_{14} & -0.58 x_{31} & -0.54 x_{18} & +  0.59 x_{34} & -0.23 x_{29} & -0.82 x_{25} & +  2.66 x_{6} & +  0.30 x_{32}\\
 x_{2}   &  0.0753090665756 & +  0.01 x_{33} & +  0.89 x_{13} & +  1.41 x_{8} & +  0.20 x_{4} & +  1.01 x_{5} & -0.00 x_{22} & +  0.06 x_{17} & +  0.02 x_{14} & -0.01 x_{31} & -0.03 x_{18} & +  0.06 x_{34} & +  0.04 x_{29} & -0.01 x_{25} & +  0.90 x_{6} & +  0.05 x_{32}\\
 x_{1}   &  0.111921160358 & +  0.09 x_{33} & -0.52 x_{13} & -1.62 x_{8} & +  2.43 x_{4} & -0.69 x_{5} & +  0.04 x_{22} & -0.02 x_{17} & +  0.39 x_{14} & +  0.03 x_{31} & +  0.12 x_{18} & -0.02 x_{34} & +  0.07 x_{29} & +  0.04 x_{25} & -1.08 x_{6} & -0.09 x_{32}\\
 x_{3}   &  0.144640329586 & +  0.00 x_{33} & -0.50 x_{13} & +  0.29 x_{8} & +  1.15 x_{4} & -0.21 x_{5} & +  0.01 x_{22} & -0.03 x_{17} & -0.86 x_{14} & +  0.04 x_{31} & +  0.01 x_{18} & +  0.01 x_{34} & +  0.02 x_{29} & +  0.06 x_{25} & -0.14 x_{6} & +  0.02 x_{32}\\
 x_{23}   &  0.284878416613 & +  1.02 x_{33} & -1.93 x_{13} & -15.07 x_{8} & +  0.75 x_{4} & -5.23 x_{5} & +  0.12 x_{22} & -0.55 x_{17} & -10.95 x_{14} & +  0.02 x_{31} & +  0.58 x_{18} & +  0.08 x_{34} & +  0.11 x_{29} & +  0.16 x_{25} & -0.56 x_{6} & -0.00 x_{32}\\
 x_{7}   &  0.00944964285448 & -0.04 x_{33} & +  1.13 x_{13} & +  2.54 x_{8} & -0.77 x_{4} & +  1.93 x_{5} & -0.06 x_{22} & +  0.07 x_{17} & +  0.08 x_{14} & +  0.02 x_{31} & -0.10 x_{18} & +  0.04 x_{34} & +  0.03 x_{29} & -0.03 x_{25} & +  2.13 x_{6} & +  0.09 x_{32}\\
\hline
z    &  -1.01956604216 & -0.20 x_{33} & -1.02 x_{13} & -3.65 x_{8} & -4.36 x_{4} & -5.01 x_{5} & -0.02 x_{22} & -0.00 x_{17} & -0.06 x_{14} & -0.15 x_{31} & -0.05 x_{18} & -0.07 x_{34} & -0.25 x_{29} & -0.02 x_{25} & -4.57 x_{6} & -0.14 x_{32}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{16}   &  8.00864603917 & -0.08 x_{33} & +  5.53 x_{13} & + 17.57 x_{8} & + 10.74 x_{4} & + 21.28 x_{5} & +  0.55 x_{22} & +  0.74 x_{17} & -2.50 x_{14} & +  1.06 x_{31} & -0.48 x_{18} & +  1.02 x_{34} & +  1.37 x_{29} & +  0.13 x_{25} & + 33.18 x_{6} & +  0.93 x_{32}\\
 x_{15}   &  0.0745432908887 & -0.01 x_{33} & -0.02 x_{13} & +  0.10 x_{8} & -0.28 x_{4} & +  0.22 x_{5} & +  0.04 x_{22} & +  0.02 x_{17} & -0.20 x_{14} & +  0.02 x_{31} & +  0.03 x_{18} & -0.02 x_{34} & -0.02 x_{29} & -0.02 x_{25} & +  0.25 x_{6} & +  0.03 x_{32}\\
 x_{9}   &  0.281173975013 & +  0.01 x_{33} & +  0.21 x_{13} & +  0.27 x_{8} & +  0.71 x_{4} & +  0.24 x_{5} & +  0.03 x_{22} & +  0.00 x_{17} & -0.04 x_{14} & +  0.05 x_{31} & -0.01 x_{18} & +  0.03 x_{34} & +  0.02 x_{29} & -0.01 x_{25} & +  0.26 x_{6} & -0.01 x_{32}\\
 x_{19}   &  6.66236932572 & +  0.52 x_{33} & -9.98 x_{13} & -27.54 x_{8} & + 37.19 x_{4} & -20.01 x_{5} & +  1.32 x_{22} & -0.88 x_{17} & +  2.13 x_{14} & +  1.38 x_{31} & +  0.76 x_{18} & -0.33 x_{34} & +  0.68 x_{29} & +  1.34 x_{25} & -18.06 x_{6} & -0.86 x_{32}\\
 x_{11}   &  0.00523102270954 & +  0.10 x_{33} & -0.66 x_{13} & -0.59 x_{8} & -0.54 x_{4} & +  0.54 x_{5} & -0.05 x_{22} & -0.05 x_{17} & +  0.32 x_{14} & -0.03 x_{31} & +  0.03 x_{18} & -0.04 x_{34} & -0.00 x_{29} & -0.03 x_{25} & +  0.11 x_{6} & -0.01 x_{32}\\
 x_{21}   &  6.40272113021 & -0.44 x_{33} & + 10.17 x_{13} & + 13.77 x_{8} & + 11.01 x_{4} & +  6.94 x_{5} & +  0.89 x_{22} & +  0.63 x_{17} & -1.50 x_{14} & +  0.86 x_{31} & -0.11 x_{18} & +  0.75 x_{34} & +  0.38 x_{29} & +  0.21 x_{25} & +  5.48 x_{6} & +  0.95 x_{32}\\
 x_{30}   &  2.96272483932 & -1.00 x_{33} & +  8.50 x_{13} & + 34.91 x_{8} & + 25.78 x_{4} & +  1.43 x_{5} & -0.04 x_{22} & +  0.45 x_{17} & -13.36 x_{14} & +  0.63 x_{31} & -0.92 x_{18} & +  1.35 x_{34} & +  0.79 x_{29} & +  0.38 x_{25} & +  1.41 x_{6} & +  0.68 x_{32}\\
 x_{27}   &  1.41904428752 & +  0.41 x_{33} & -3.62 x_{13} & + 11.91 x_{8} & -2.28 x_{4} & + 13.06 x_{5} & -0.64 x_{22} & -0.49 x_{17} & -7.42 x_{14} & +  0.30 x_{31} & -0.19 x_{18} & -0.26 x_{34} & +  0.56 x_{29} & -0.16 x_{25} & + 22.91 x_{6} & +  0.60 x_{32}\\
 x_{20}   &  5.65104462738 & +  1.09 x_{33} & -14.61 x_{13} & -24.59 x_{8} & + 29.39 x_{4} & -4.45 x_{5} & +  0.86 x_{22} & -1.01 x_{17} & -10.62 x_{14} & +  0.52 x_{31} & +  1.70 x_{18} & -0.23 x_{34} & +  0.93 x_{29} & +  0.53 x_{25} & -23.82 x_{6} & -1.11 x_{32}\\
 x_{10}   &  0.13177966004 & +  0.05 x_{33} & -0.80 x_{13} & -0.38 x_{8} & +  1.13 x_{4} & +  0.27 x_{5} & +  0.03 x_{22} & -0.04 x_{17} & +  0.05 x_{14} & +  0.03 x_{31} & +  0.01 x_{18} & -0.02 x_{34} & +  0.07 x_{29} & +  0.05 x_{25} & +  0.45 x_{6} & +  0.01 x_{32}\\
 x_{26}   &  0.909412281081 & -1.33 x_{33} & +  7.81 x_{13} & + 15.62 x_{8} & -7.94 x_{4} & -21.95 x_{5} & +  0.96 x_{22} & +  0.37 x_{17} & -3.49 x_{14} & +  0.21 x_{31} & -0.64 x_{18} & +  0.41 x_{34} & -0.80 x_{29} & +  0.59 x_{25} & -15.13 x_{6} & +  0.39 x_{32}\\
 x_{12}   &  0.185517894132 & -0.03 x_{33} & +  0.30 x_{13} & +  0.64 x_{8} & -0.67 x_{4} & +  0.70 x_{5} & -0.03 x_{22} & -0.01 x_{17} & -0.71 x_{14} & -0.02 x_{31} & -0.01 x_{18} & +  0.02 x_{34} & +  0.02 x_{29} & -0.04 x_{25} & +  0.68 x_{6} & +  0.05 x_{32}\\
 x_{28}   &  1.85251730507 & +  0.40 x_{33} & -1.87 x_{13} & +  3.53 x_{8} & -0.41 x_{4} & +  3.63 x_{5} & +  0.36 x_{22} & -0.34 x_{17} & -8.27 x_{14} & -0.28 x_{31} & +  0.33 x_{18} & -0.18 x_{34} & -0.06 x_{29} & +  0.60 x_{25} & +  1.54 x_{6} & +  0.39 x_{32}\\
 x_{24}   &  0.59054637452 & +  0.13 x_{33} & + 13.02 x_{13} & +  6.69 x_{8} & -11.42 x_{4} & +  7.44 x_{5} & -1.13 x_{22} & +  0.10 x_{17} & -10.55 x_{14} & -0.58 x_{31} & -0.54 x_{18} & +  0.59 x_{34} & -0.23 x_{29} & -0.82 x_{25} & +  2.66 x_{6} & +  0.30 x_{32}\\
 x_{2}   &  0.0753090665756 & +  0.01 x_{33} & +  0.89 x_{13} & +  1.41 x_{8} & +  0.20 x_{4} & +  1.01 x_{5} & -0.00 x_{22} & +  0.06 x_{17} & +  0.02 x_{14} & -0.01 x_{31} & -0.03 x_{18} & +  0.06 x_{34} & +  0.04 x_{29} & -0.01 x_{25} & +  0.90 x_{6} & +  0.05 x_{32}\\
 x_{1}   &  0.111921160358 & +  0.09 x_{33} & -0.52 x_{13} & -1.62 x_{8} & +  2.43 x_{4} & -0.69 x_{5} & +  0.04 x_{22} & -0.02 x_{17} & +  0.39 x_{14} & +  0.03 x_{31} & +  0.12 x_{18} & -0.02 x_{34} & +  0.07 x_{29} & +  0.04 x_{25} & -1.08 x_{6} & -0.09 x_{32}\\
 x_{3}   &  0.144640329586 & +  0.00 x_{33} & -0.50 x_{13} & +  0.29 x_{8} & +  1.15 x_{4} & -0.21 x_{5} & +  0.01 x_{22} & -0.03 x_{17} & -0.86 x_{14} & +  0.04 x_{31} & +  0.01 x_{18} & +  0.01 x_{34} & +  0.02 x_{29} & +  0.06 x_{25} & -0.14 x_{6} & +  0.02 x_{32}\\
 x_{23}   &  0.284878416613 & +  1.02 x_{33} & -1.93 x_{13} & -15.07 x_{8} & +  0.75 x_{4} & -5.23 x_{5} & +  0.12 x_{22} & -0.55 x_{17} & -10.95 x_{14} & +  0.02 x_{31} & +  0.58 x_{18} & +  0.08 x_{34} & +  0.11 x_{29} & +  0.16 x_{25} & -0.56 x_{6} & -0.00 x_{32}\\
 x_{7}   &  0.00944964285448 & -0.04 x_{33} & +  1.13 x_{13} & +  2.54 x_{8} & -0.77 x_{4} & +  1.93 x_{5} & -0.06 x_{22} & +  0.07 x_{17} & +  0.08 x_{14} & +  0.02 x_{31} & -0.10 x_{18} & +  0.04 x_{34} & +  0.03 x_{29} & -0.03 x_{25} & +  2.13 x_{6} & +  0.09 x_{32}\\
\hline
z    &  -1.95011575783 & -0.50 x_{33} & -5.59 x_{13} & -5.13 x_{8} & -2.18 x_{4} & +  0.24 x_{5} & -0.22 x_{22} & -0.08 x_{17} & -0.24 x_{14} & -0.17 x_{31} & -0.49 x_{18} & -0.15 x_{34} & -0.18 x_{29} & +  0.11 x_{25} & -2.71 x_{6} & -0.02 x_{32}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{16}   &  8.00864603917 & -0.08 x_{33} & +  5.53 x_{13} & + 17.57 x_{8} & + 10.74 x_{4} & + 21.28 x_{5} & +  0.55 x_{22} & +  0.74 x_{17} & -2.50 x_{14} & +  1.06 x_{31} & -0.48 x_{18} & +  1.02 x_{34} & +  1.37 x_{29} & +  0.13 x_{25} & + 33.18 x_{6} & +  0.93 x_{32}\\
 x_{15}   &  0.0745432908887 & -0.01 x_{33} & -0.02 x_{13} & +  0.10 x_{8} & -0.28 x_{4} & +  0.22 x_{5} & +  0.04 x_{22} & +  0.02 x_{17} & -0.20 x_{14} & +  0.02 x_{31} & +  0.03 x_{18} & -0.02 x_{34} & -0.02 x_{29} & -0.02 x_{25} & +  0.25 x_{6} & +  0.03 x_{32}\\
 x_{9}   &  0.281173975013 & +  0.01 x_{33} & +  0.21 x_{13} & +  0.27 x_{8} & +  0.71 x_{4} & +  0.24 x_{5} & +  0.03 x_{22} & +  0.00 x_{17} & -0.04 x_{14} & +  0.05 x_{31} & -0.01 x_{18} & +  0.03 x_{34} & +  0.02 x_{29} & -0.01 x_{25} & +  0.26 x_{6} & -0.01 x_{32}\\
 x_{19}   &  6.66236932572 & +  0.52 x_{33} & -9.98 x_{13} & -27.54 x_{8} & + 37.19 x_{4} & -20.01 x_{5} & +  1.32 x_{22} & -0.88 x_{17} & +  2.13 x_{14} & +  1.38 x_{31} & +  0.76 x_{18} & -0.33 x_{34} & +  0.68 x_{29} & +  1.34 x_{25} & -18.06 x_{6} & -0.86 x_{32}\\
 x_{11}   &  0.00523102270954 & +  0.10 x_{33} & -0.66 x_{13} & -0.59 x_{8} & -0.54 x_{4} & +  0.54 x_{5} & -0.05 x_{22} & -0.05 x_{17} & +  0.32 x_{14} & -0.03 x_{31} & +  0.03 x_{18} & -0.04 x_{34} & -0.00 x_{29} & -0.03 x_{25} & +  0.11 x_{6} & -0.01 x_{32}\\
 x_{21}   &  6.40272113021 & -0.44 x_{33} & + 10.17 x_{13} & + 13.77 x_{8} & + 11.01 x_{4} & +  6.94 x_{5} & +  0.89 x_{22} & +  0.63 x_{17} & -1.50 x_{14} & +  0.86 x_{31} & -0.11 x_{18} & +  0.75 x_{34} & +  0.38 x_{29} & +  0.21 x_{25} & +  5.48 x_{6} & +  0.95 x_{32}\\
 x_{30}   &  2.96272483932 & -1.00 x_{33} & +  8.50 x_{13} & + 34.91 x_{8} & + 25.78 x_{4} & +  1.43 x_{5} & -0.04 x_{22} & +  0.45 x_{17} & -13.36 x_{14} & +  0.63 x_{31} & -0.92 x_{18} & +  1.35 x_{34} & +  0.79 x_{29} & +  0.38 x_{25} & +  1.41 x_{6} & +  0.68 x_{32}\\
 x_{27}   &  1.41904428752 & +  0.41 x_{33} & -3.62 x_{13} & + 11.91 x_{8} & -2.28 x_{4} & + 13.06 x_{5} & -0.64 x_{22} & -0.49 x_{17} & -7.42 x_{14} & +  0.30 x_{31} & -0.19 x_{18} & -0.26 x_{34} & +  0.56 x_{29} & -0.16 x_{25} & + 22.91 x_{6} & +  0.60 x_{32}\\
 x_{20}   &  5.65104462738 & +  1.09 x_{33} & -14.61 x_{13} & -24.59 x_{8} & + 29.39 x_{4} & -4.45 x_{5} & +  0.86 x_{22} & -1.01 x_{17} & -10.62 x_{14} & +  0.52 x_{31} & +  1.70 x_{18} & -0.23 x_{34} & +  0.93 x_{29} & +  0.53 x_{25} & -23.82 x_{6} & -1.11 x_{32}\\
 x_{10}   &  0.13177966004 & +  0.05 x_{33} & -0.80 x_{13} & -0.38 x_{8} & +  1.13 x_{4} & +  0.27 x_{5} & +  0.03 x_{22} & -0.04 x_{17} & +  0.05 x_{14} & +  0.03 x_{31} & +  0.01 x_{18} & -0.02 x_{34} & +  0.07 x_{29} & +  0.05 x_{25} & +  0.45 x_{6} & +  0.01 x_{32}\\
 x_{26}   &  0.909412281081 & -1.33 x_{33} & +  7.81 x_{13} & + 15.62 x_{8} & -7.94 x_{4} & -21.95 x_{5} & +  0.96 x_{22} & +  0.37 x_{17} & -3.49 x_{14} & +  0.21 x_{31} & -0.64 x_{18} & +  0.41 x_{34} & -0.80 x_{29} & +  0.59 x_{25} & -15.13 x_{6} & +  0.39 x_{32}\\
 x_{12}   &  0.185517894132 & -0.03 x_{33} & +  0.30 x_{13} & +  0.64 x_{8} & -0.67 x_{4} & +  0.70 x_{5} & -0.03 x_{22} & -0.01 x_{17} & -0.71 x_{14} & -0.02 x_{31} & -0.01 x_{18} & +  0.02 x_{34} & +  0.02 x_{29} & -0.04 x_{25} & +  0.68 x_{6} & +  0.05 x_{32}\\
 x_{28}   &  1.85251730507 & +  0.40 x_{33} & -1.87 x_{13} & +  3.53 x_{8} & -0.41 x_{4} & +  3.63 x_{5} & +  0.36 x_{22} & -0.34 x_{17} & -8.27 x_{14} & -0.28 x_{31} & +  0.33 x_{18} & -0.18 x_{34} & -0.06 x_{29} & +  0.60 x_{25} & +  1.54 x_{6} & +  0.39 x_{32}\\
 x_{24}   &  0.59054637452 & +  0.13 x_{33} & + 13.02 x_{13} & +  6.69 x_{8} & -11.42 x_{4} & +  7.44 x_{5} & -1.13 x_{22} & +  0.10 x_{17} & -10.55 x_{14} & -0.58 x_{31} & -0.54 x_{18} & +  0.59 x_{34} & -0.23 x_{29} & -0.82 x_{25} & +  2.66 x_{6} & +  0.30 x_{32}\\
 x_{2}   &  0.0753090665756 & +  0.01 x_{33} & +  0.89 x_{13} & +  1.41 x_{8} & +  0.20 x_{4} & +  1.01 x_{5} & -0.00 x_{22} & +  0.06 x_{17} & +  0.02 x_{14} & -0.01 x_{31} & -0.03 x_{18} & +  0.06 x_{34} & +  0.04 x_{29} & -0.01 x_{25} & +  0.90 x_{6} & +  0.05 x_{32}\\
 x_{1}   &  0.111921160358 & +  0.09 x_{33} & -0.52 x_{13} & -1.62 x_{8} & +  2.43 x_{4} & -0.69 x_{5} & +  0.04 x_{22} & -0.02 x_{17} & +  0.39 x_{14} & +  0.03 x_{31} & +  0.12 x_{18} & -0.02 x_{34} & +  0.07 x_{29} & +  0.04 x_{25} & -1.08 x_{6} & -0.09 x_{32}\\
 x_{3}   &  0.144640329586 & +  0.00 x_{33} & -0.50 x_{13} & +  0.29 x_{8} & +  1.15 x_{4} & -0.21 x_{5} & +  0.01 x_{22} & -0.03 x_{17} & -0.86 x_{14} & +  0.04 x_{31} & +  0.01 x_{18} & +  0.01 x_{34} & +  0.02 x_{29} & +  0.06 x_{25} & -0.14 x_{6} & +  0.02 x_{32}\\
 x_{23}   &  0.284878416613 & +  1.02 x_{33} & -1.93 x_{13} & -15.07 x_{8} & +  0.75 x_{4} & -5.23 x_{5} & +  0.12 x_{22} & -0.55 x_{17} & -10.95 x_{14} & +  0.02 x_{31} & +  0.58 x_{18} & +  0.08 x_{34} & +  0.11 x_{29} & +  0.16 x_{25} & -0.56 x_{6} & -0.00 x_{32}\\
 x_{7}   &  0.00944964285448 & -0.04 x_{33} & +  1.13 x_{13} & +  2.54 x_{8} & -0.77 x_{4} & +  1.93 x_{5} & -0.06 x_{22} & +  0.07 x_{17} & +  0.08 x_{14} & +  0.02 x_{31} & -0.10 x_{18} & +  0.04 x_{34} & +  0.03 x_{29} & -0.03 x_{25} & +  2.13 x_{6} & +  0.09 x_{32}\\
\hline
z    &  -1.95011575783 & -0.50 x_{33} & -5.59 x_{13} & -5.13 x_{8} & -2.18 x_{4} & +  0.24 x_{5} & -0.22 x_{22} & -0.08 x_{17} & -0.24 x_{14} & -0.17 x_{31} & -0.49 x_{18} & -0.15 x_{34} & -0.18 x_{29} & +  0.11 x_{25} & -2.71 x_{6} & -0.02 x_{32}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{26} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{16}   &  8.89039861512 & -1.37 x_{33} & + 13.11 x_{13} & + 32.71 x_{8} & +  3.04 x_{4} & -0.97 x_{26} & +  1.49 x_{22} & +  1.09 x_{17} & -5.88 x_{14} & +  1.26 x_{31} & -1.10 x_{18} & +  1.42 x_{34} & +  0.59 x_{29} & +  0.70 x_{25} & + 18.51 x_{6} & +  1.31 x_{32}\\
 x_{15}   &  0.0834555541214 & -0.02 x_{33} & +  0.05 x_{13} & +  0.25 x_{8} & -0.36 x_{4} & -0.01 x_{26} & +  0.05 x_{22} & +  0.03 x_{17} & -0.24 x_{14} & +  0.03 x_{31} & +  0.02 x_{18} & -0.02 x_{34} & -0.03 x_{29} & -0.01 x_{25} & +  0.10 x_{6} & +  0.03 x_{32}\\
 x_{9}   &  0.290915661812 & -0.00 x_{33} & +  0.29 x_{13} & +  0.44 x_{8} & +  0.62 x_{4} & -0.01 x_{26} & +  0.04 x_{22} & +  0.01 x_{17} & -0.07 x_{14} & +  0.05 x_{31} & -0.01 x_{18} & +  0.03 x_{34} & +  0.01 x_{29} & -0.00 x_{25} & +  0.10 x_{6} & -0.00 x_{32}\\
 x_{19}   &  5.83319261529 & +  1.73 x_{33} & -17.10 x_{13} & -41.78 x_{8} & + 44.43 x_{4} & +  0.91 x_{26} & +  0.45 x_{22} & -1.21 x_{17} & +  5.32 x_{14} & +  1.20 x_{31} & +  1.34 x_{18} & -0.71 x_{34} & +  1.41 x_{29} & +  0.81 x_{25} & -4.26 x_{6} & -1.22 x_{32}\\
 x_{11}   &  0.0276892366467 & +  0.07 x_{33} & -0.47 x_{13} & -0.20 x_{8} & -0.74 x_{4} & -0.02 x_{26} & -0.03 x_{22} & -0.04 x_{17} & +  0.23 x_{14} & -0.02 x_{31} & +  0.02 x_{18} & -0.03 x_{34} & -0.02 x_{29} & -0.01 x_{25} & -0.26 x_{6} & -0.00 x_{32}\\
 x_{21}   &  6.69025566544 & -0.86 x_{33} & + 12.64 x_{13} & + 18.71 x_{8} & +  8.50 x_{4} & -0.32 x_{26} & +  1.20 x_{22} & +  0.75 x_{17} & -2.60 x_{14} & +  0.93 x_{31} & -0.32 x_{18} & +  0.88 x_{34} & +  0.12 x_{29} & +  0.40 x_{25} & +  0.70 x_{6} & +  1.08 x_{32}\\
 x_{30}   &  3.02190263076 & -1.09 x_{33} & +  9.01 x_{13} & + 35.93 x_{8} & + 25.26 x_{4} & -0.07 x_{26} & +  0.02 x_{22} & +  0.47 x_{17} & -13.59 x_{14} & +  0.64 x_{31} & -0.96 x_{18} & +  1.38 x_{34} & +  0.74 x_{29} & +  0.42 x_{25} & +  0.43 x_{6} & +  0.71 x_{32}\\
 x_{27}   &  1.96030443676 & -0.38 x_{33} & +  1.03 x_{13} & + 21.20 x_{8} & -7.00 x_{4} & -0.60 x_{26} & -0.07 x_{22} & -0.28 x_{17} & -9.50 x_{14} & +  0.42 x_{31} & -0.57 x_{18} & -0.01 x_{34} & +  0.08 x_{29} & +  0.18 x_{25} & + 13.90 x_{6} & +  0.83 x_{32}\\
 x_{20}   &  5.46685320941 & +  1.36 x_{33} & -16.19 x_{13} & -27.76 x_{8} & + 31.00 x_{4} & +  0.20 x_{26} & +  0.66 x_{22} & -1.08 x_{17} & -9.92 x_{14} & +  0.48 x_{31} & +  1.83 x_{18} & -0.32 x_{34} & +  1.09 x_{29} & +  0.41 x_{25} & -20.75 x_{6} & -1.19 x_{32}\\
 x_{10}   &  0.142928813668 & +  0.04 x_{33} & -0.70 x_{13} & -0.19 x_{8} & +  1.03 x_{4} & -0.01 x_{26} & +  0.04 x_{22} & -0.04 x_{17} & +  0.01 x_{14} & +  0.04 x_{31} & -0.00 x_{18} & -0.01 x_{34} & +  0.06 x_{29} & +  0.06 x_{25} & +  0.26 x_{6} & +  0.02 x_{32}\\
 x_{5}   &  0.0414283664121 & -0.06 x_{33} & +  0.36 x_{13} & +  0.71 x_{8} & -0.36 x_{4} & -0.05 x_{26} & +  0.04 x_{22} & +  0.02 x_{17} & -0.16 x_{14} & +  0.01 x_{31} & -0.03 x_{18} & +  0.02 x_{34} & -0.04 x_{29} & +  0.03 x_{25} & -0.69 x_{6} & +  0.02 x_{32}\\
 x_{12}   &  0.214706370574 & -0.07 x_{33} & +  0.56 x_{13} & +  1.15 x_{8} & -0.92 x_{4} & -0.03 x_{26} & -0.00 x_{22} & +  0.00 x_{17} & -0.83 x_{14} & -0.01 x_{31} & -0.03 x_{18} & +  0.04 x_{34} & -0.01 x_{29} & -0.02 x_{25} & +  0.20 x_{6} & +  0.07 x_{32}\\
 x_{28}   &  2.00280962042 & +  0.18 x_{33} & -0.58 x_{13} & +  6.11 x_{8} & -1.72 x_{4} & -0.17 x_{26} & +  0.52 x_{22} & -0.28 x_{17} & -8.85 x_{14} & -0.24 x_{31} & +  0.22 x_{18} & -0.11 x_{34} & -0.20 x_{29} & +  0.70 x_{25} & -0.96 x_{6} & +  0.45 x_{32}\\
 x_{24}   &  0.89881860036 & -0.32 x_{33} & + 15.67 x_{13} & + 11.99 x_{8} & -14.11 x_{4} & -0.34 x_{26} & -0.81 x_{22} & +  0.22 x_{17} & -11.73 x_{14} & -0.51 x_{31} & -0.76 x_{18} & +  0.73 x_{34} & -0.50 x_{29} & -0.62 x_{25} & -2.47 x_{6} & +  0.44 x_{32}\\
 x_{2}   &  0.117292840947 & -0.05 x_{33} & +  1.25 x_{13} & +  2.13 x_{8} & -0.16 x_{4} & -0.05 x_{26} & +  0.04 x_{22} & +  0.07 x_{17} & -0.14 x_{14} & +  0.00 x_{31} & -0.06 x_{18} & +  0.08 x_{34} & +  0.00 x_{29} & +  0.02 x_{25} & +  0.21 x_{6} & +  0.07 x_{32}\\
 x_{1}   &  0.083274770342 & +  0.14 x_{33} & -0.77 x_{13} & -2.11 x_{8} & +  2.68 x_{4} & +  0.03 x_{26} & +  0.01 x_{22} & -0.03 x_{17} & +  0.50 x_{14} & +  0.03 x_{31} & +  0.14 x_{18} & -0.03 x_{34} & +  0.10 x_{29} & +  0.03 x_{25} & -0.61 x_{6} & -0.10 x_{32}\\
 x_{3}   &  0.136021913984 & +  0.01 x_{33} & -0.57 x_{13} & +  0.14 x_{8} & +  1.23 x_{4} & +  0.01 x_{26} & +  0.00 x_{22} & -0.03 x_{17} & -0.83 x_{14} & +  0.04 x_{31} & +  0.02 x_{18} & +  0.01 x_{34} & +  0.03 x_{29} & +  0.05 x_{25} & +  0.01 x_{6} & +  0.01 x_{32}\\
 x_{23}   &  0.0681457368997 & +  1.34 x_{33} & -3.79 x_{13} & -18.79 x_{8} & +  2.64 x_{4} & +  0.24 x_{26} & -0.11 x_{22} & -0.64 x_{17} & -10.12 x_{14} & -0.03 x_{31} & +  0.73 x_{18} & -0.01 x_{34} & +  0.30 x_{29} & +  0.02 x_{25} & +  3.05 x_{6} & -0.10 x_{32}\\
 x_{7}   &  0.0894822069361 & -0.15 x_{33} & +  1.82 x_{13} & +  3.91 x_{8} & -1.47 x_{4} & -0.09 x_{26} & +  0.03 x_{22} & +  0.10 x_{17} & -0.22 x_{14} & +  0.03 x_{31} & -0.16 x_{18} & +  0.07 x_{34} & -0.04 x_{29} & +  0.02 x_{25} & +  0.80 x_{6} & +  0.12 x_{32}\\
\hline
z    &  -1.94029371538 & -0.52 x_{33} & -5.50 x_{13} & -4.96 x_{8} & -2.26 x_{4} & -0.01 x_{26} & -0.21 x_{22} & -0.08 x_{17} & -0.28 x_{14} & -0.17 x_{31} & -0.49 x_{18} & -0.15 x_{34} & -0.19 x_{29} & +  0.12 x_{25} & -2.87 x_{6} & -0.01 x_{32}\\
\end{array}\]


 $ x_{25} $ enters and $ x_{24} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{16}   &  9.90726280268 & -1.74 x_{33} & + 30.84 x_{13} & + 46.28 x_{8} & -12.92 x_{4} & -1.35 x_{26} & +  0.57 x_{22} & +  1.34 x_{17} & -19.15 x_{14} & +  0.68 x_{31} & -1.96 x_{18} & +  2.25 x_{34} & +  0.02 x_{29} & -1.13 x_{24} & + 15.72 x_{6} & +  1.81 x_{32}\\
 x_{15}   &  0.0675573333745 & -0.02 x_{33} & -0.22 x_{13} & +  0.04 x_{8} & -0.11 x_{4} & -0.00 x_{26} & +  0.06 x_{22} & +  0.02 x_{17} & -0.03 x_{14} & +  0.04 x_{31} & +  0.03 x_{18} & -0.03 x_{34} & -0.02 x_{29} & +  0.02 x_{24} & +  0.14 x_{6} & +  0.03 x_{32}\\
 x_{9}   &  0.285505596887 & +  0.00 x_{33} & +  0.20 x_{13} & +  0.37 x_{8} & +  0.71 x_{4} & -0.01 x_{26} & +  0.05 x_{22} & +  0.01 x_{17} & -0.00 x_{14} & +  0.06 x_{31} & -0.01 x_{18} & +  0.03 x_{34} & +  0.01 x_{29} & +  0.01 x_{24} & +  0.11 x_{6} & -0.01 x_{32}\\
 x_{19}   &  7.00606875126 & +  1.31 x_{33} & +  3.34 x_{13} & -26.13 x_{8} & + 26.01 x_{4} & +  0.47 x_{26} & -0.61 x_{22} & -0.92 x_{17} & -9.99 x_{14} & +  0.52 x_{31} & +  0.35 x_{18} & +  0.25 x_{34} & +  0.76 x_{29} & -1.30 x_{24} & -7.48 x_{6} & -0.65 x_{32}\\
 x_{11}   &  0.00681472738512 & +  0.07 x_{33} & -0.83 x_{13} & -0.48 x_{8} & -0.41 x_{4} & -0.02 x_{26} & -0.01 x_{22} & -0.05 x_{17} & +  0.50 x_{14} & -0.01 x_{31} & +  0.03 x_{18} & -0.05 x_{34} & -0.01 x_{29} & +  0.02 x_{24} & -0.20 x_{6} & -0.01 x_{32}\\
 x_{21}   &  7.26498113151 & -1.07 x_{33} & + 22.66 x_{13} & + 26.37 x_{8} & -0.52 x_{4} & -0.53 x_{26} & +  0.68 x_{22} & +  0.89 x_{17} & -10.10 x_{14} & +  0.60 x_{31} & -0.80 x_{18} & +  1.35 x_{34} & -0.20 x_{29} & -0.64 x_{24} & -0.88 x_{6} & +  1.36 x_{32}\\
 x_{30}   &  3.62935050901 & -1.30 x_{33} & + 19.60 x_{13} & + 44.03 x_{8} & + 15.72 x_{4} & -0.29 x_{26} & -0.52 x_{22} & +  0.62 x_{17} & -21.52 x_{14} & +  0.29 x_{31} & -1.47 x_{18} & +  1.88 x_{34} & +  0.40 x_{29} & -0.68 x_{24} & -1.24 x_{6} & +  1.01 x_{32}\\
 x_{27}   &  2.227994327 & -0.48 x_{33} & +  5.70 x_{13} & + 24.77 x_{8} & -11.21 x_{4} & -0.70 x_{26} & -0.31 x_{22} & -0.21 x_{17} & -12.99 x_{14} & +  0.27 x_{31} & -0.80 x_{18} & +  0.20 x_{34} & -0.07 x_{29} & -0.30 x_{24} & + 13.16 x_{6} & +  0.96 x_{32}\\
 x_{20}   &  6.06485031117 & +  1.14 x_{33} & -5.77 x_{13} & -19.78 x_{8} & + 21.61 x_{4} & -0.02 x_{26} & +  0.13 x_{22} & -0.93 x_{17} & -17.72 x_{14} & +  0.14 x_{31} & +  1.32 x_{18} & +  0.17 x_{34} & +  0.75 x_{29} & -0.67 x_{24} & -22.40 x_{6} & -0.90 x_{32}\\
 x_{10}   &  0.231591511802 & +  0.01 x_{33} & +  0.84 x_{13} & +  0.99 x_{8} & -0.36 x_{4} & -0.05 x_{26} & -0.04 x_{22} & -0.02 x_{17} & -1.15 x_{14} & -0.01 x_{31} & -0.08 x_{18} & +  0.06 x_{34} & +  0.01 x_{29} & -0.10 x_{24} & +  0.02 x_{6} & +  0.06 x_{32}\\
 x_{5}   &  0.0802133625845 & -0.07 x_{33} & +  1.03 x_{13} & +  1.23 x_{8} & -0.97 x_{4} & -0.06 x_{26} & +  0.01 x_{22} & +  0.03 x_{17} & -0.67 x_{14} & -0.01 x_{31} & -0.06 x_{18} & +  0.05 x_{34} & -0.06 x_{29} & -0.04 x_{24} & -0.80 x_{6} & +  0.04 x_{32}\\
 x_{12}   &  0.186023063011 & -0.06 x_{33} & +  0.06 x_{13} & +  0.76 x_{8} & -0.47 x_{4} & -0.02 x_{26} & +  0.02 x_{22} & -0.01 x_{17} & -0.45 x_{14} & +  0.00 x_{31} & -0.01 x_{18} & +  0.01 x_{34} & +  0.01 x_{29} & +  0.03 x_{24} & +  0.27 x_{6} & +  0.05 x_{32}\\
 x_{28}   &  3.01804443117 & -0.19 x_{33} & + 17.12 x_{13} & + 19.65 x_{8} & -17.66 x_{4} & -0.55 x_{26} & -0.39 x_{22} & -0.03 x_{17} & -22.10 x_{14} & -0.82 x_{31} & -0.63 x_{18} & +  0.72 x_{34} & -0.77 x_{29} & -1.13 x_{24} & -3.75 x_{6} & +  0.95 x_{32}\\
 x_{25}   &  1.45219483033 & -0.52 x_{33} & + 25.32 x_{13} & + 19.37 x_{8} & -22.80 x_{4} & -0.55 x_{26} & -1.30 x_{22} & +  0.36 x_{17} & -18.95 x_{14} & -0.83 x_{31} & -1.23 x_{18} & +  1.19 x_{34} & -0.81 x_{29} & -1.62 x_{24} & -3.98 x_{6} & +  0.71 x_{32}\\
 x_{2}   &  0.144888684021 & -0.06 x_{33} & +  1.73 x_{13} & +  2.50 x_{8} & -0.59 x_{4} & -0.06 x_{26} & +  0.02 x_{22} & +  0.08 x_{17} & -0.50 x_{14} & -0.01 x_{31} & -0.08 x_{18} & +  0.10 x_{34} & -0.01 x_{29} & -0.03 x_{24} & +  0.13 x_{6} & +  0.08 x_{32}\\
 x_{1}   &  0.12113701186 & +  0.12 x_{33} & -0.11 x_{13} & -1.61 x_{8} & +  2.09 x_{4} & +  0.02 x_{26} & -0.02 x_{22} & -0.02 x_{17} & +  0.01 x_{14} & +  0.01 x_{31} & +  0.11 x_{18} & +  0.00 x_{34} & +  0.08 x_{29} & -0.04 x_{24} & -0.71 x_{6} & -0.09 x_{32}\\
 x_{3}   &  0.210347649812 & -0.01 x_{33} & +  0.72 x_{13} & +  1.13 x_{8} & +  0.06 x_{4} & -0.02 x_{26} & -0.06 x_{22} & -0.01 x_{17} & -1.80 x_{14} & -0.00 x_{31} & -0.04 x_{18} & +  0.07 x_{34} & -0.01 x_{29} & -0.08 x_{24} & -0.20 x_{6} & +  0.05 x_{32}\\
 x_{23}   &  0.103117111297 & +  1.32 x_{33} & -3.18 x_{13} & -18.33 x_{8} & +  2.09 x_{4} & +  0.23 x_{26} & -0.14 x_{22} & -0.63 x_{17} & -10.57 x_{14} & -0.05 x_{31} & +  0.70 x_{18} & +  0.01 x_{34} & +  0.28 x_{29} & -0.04 x_{24} & +  2.95 x_{6} & -0.08 x_{32}\\
 x_{7}   &  0.123382430861 & -0.17 x_{33} & +  2.41 x_{13} & +  4.37 x_{8} & -2.00 x_{4} & -0.10 x_{26} & -0.00 x_{22} & +  0.11 x_{17} & -0.67 x_{14} & +  0.01 x_{31} & -0.18 x_{18} & +  0.10 x_{34} & -0.06 x_{29} & -0.04 x_{24} & +  0.71 x_{6} & +  0.14 x_{32}\\
\hline
z    &  -1.77003813969 & -0.58 x_{33} & -2.54 x_{13} & -2.69 x_{8} & -4.94 x_{4} & -0.08 x_{26} & -0.37 x_{22} & -0.04 x_{17} & -2.50 x_{14} & -0.26 x_{31} & -0.64 x_{18} & -0.01 x_{34} & -0.29 x_{29} & -0.19 x_{24} & -3.34 x_{6} & +  0.07 x_{32}\\
\end{array}\]


 $ x_{32} $ enters and $ x_{11} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{16}   &  10.9326052042 & +  9.26 x_{33} & -94.71 x_{13} & -25.92 x_{8} & -75.00 x_{4} & -3.88 x_{26} & -0.54 x_{22} & -5.67 x_{17} & + 56.77 x_{14} & -0.72 x_{31} & +  3.04 x_{18} & -4.94 x_{34} & -1.39 x_{29} & +  2.36 x_{24} & -14.85 x_{6} & -150.46 x_{11}\\
 x_{15}   &  0.0829397696069 & +  0.15 x_{33} & -2.11 x_{13} & -1.05 x_{8} & -1.04 x_{4} & -0.04 x_{26} & +  0.05 x_{22} & -0.08 x_{17} & +  1.11 x_{14} & +  0.01 x_{31} & +  0.11 x_{18} & -0.14 x_{34} & -0.04 x_{29} & +  0.07 x_{24} & -0.32 x_{6} & -2.26 x_{11}\\
 x_{9}   &  0.281986508203 & -0.04 x_{33} & +  0.63 x_{13} & +  0.61 x_{8} & +  0.92 x_{4} & +  0.00 x_{26} & +  0.05 x_{22} & +  0.03 x_{17} & -0.26 x_{14} & +  0.06 x_{31} & -0.03 x_{18} & +  0.05 x_{34} & +  0.02 x_{29} & -0.01 x_{24} & +  0.22 x_{6} & +  0.52 x_{11}\\
 x_{19}   &  6.64012947538 & -2.61 x_{33} & + 48.15 x_{13} & -0.36 x_{8} & + 48.17 x_{4} & +  1.37 x_{26} & -0.21 x_{22} & +  1.58 x_{17} & -37.09 x_{14} & +  1.02 x_{31} & -1.43 x_{18} & +  2.82 x_{34} & +  1.26 x_{29} & -2.55 x_{24} & +  3.43 x_{6} & + 53.70 x_{11}\\
 x_{32}   &  0.566728104362 & +  6.08 x_{33} & -69.39 x_{13} & -39.90 x_{8} & -34.31 x_{4} & -1.40 x_{26} & -0.62 x_{22} & -3.88 x_{17} & + 41.96 x_{14} & -0.77 x_{31} & +  2.76 x_{18} & -3.97 x_{34} & -0.78 x_{29} & +  1.93 x_{24} & -16.89 x_{6} & -83.16 x_{11}\\
 x_{21}   &  8.03368940421 & +  7.17 x_{33} & -71.46 x_{13} & -27.76 x_{8} & -47.06 x_{4} & -2.43 x_{26} & -0.15 x_{22} & -4.37 x_{17} & + 46.82 x_{14} & -0.45 x_{31} & +  2.95 x_{18} & -4.04 x_{34} & -1.26 x_{29} & +  1.98 x_{24} & -23.79 x_{6} & -112.80 x_{11}\\
 x_{30}   &  4.19895123229 & +  4.80 x_{33} & -50.14 x_{13} & +  3.93 x_{8} & -18.76 x_{4} & -1.70 x_{26} & -1.14 x_{22} & -3.27 x_{17} & + 20.66 x_{14} & -0.48 x_{31} & +  1.31 x_{18} & -2.12 x_{34} & -0.39 x_{29} & +  1.27 x_{24} & -18.22 x_{6} & -83.58 x_{11}\\
 x_{27}   &  2.77432611071 & +  5.38 x_{33} & -61.19 x_{13} & -13.70 x_{8} & -44.28 x_{4} & -2.04 x_{26} & -0.90 x_{22} & -3.95 x_{17} & + 27.47 x_{14} & -0.48 x_{31} & +  1.87 x_{18} & -3.63 x_{34} & -0.82 x_{29} & +  1.56 x_{24} & -3.12 x_{6} & -80.17 x_{11}\\
 x_{20}   &  5.55344264505 & -4.34 x_{33} & + 56.85 x_{13} & + 16.23 x_{8} & + 52.57 x_{4} & +  1.24 x_{26} & +  0.68 x_{22} & +  2.57 x_{17} & -55.59 x_{14} & +  0.83 x_{31} & -1.17 x_{18} & +  3.76 x_{34} & +  1.46 x_{29} & -2.41 x_{24} & -7.15 x_{6} & + 75.04 x_{11}\\
 x_{10}   &  0.264694477352 & +  0.36 x_{33} & -3.21 x_{13} & -1.34 x_{8} & -2.36 x_{4} & -0.13 x_{26} & -0.07 x_{22} & -0.24 x_{17} & +  1.30 x_{14} & -0.06 x_{31} & +  0.08 x_{18} & -0.17 x_{34} & -0.04 x_{29} & +  0.01 x_{24} & -0.97 x_{6} & -4.86 x_{11}\\
 x_{5}   &  0.101114843538 & +  0.15 x_{33} & -1.53 x_{13} & -0.24 x_{8} & -2.24 x_{4} & -0.11 x_{26} & -0.01 x_{22} & -0.12 x_{17} & +  0.88 x_{14} & -0.04 x_{31} & +  0.04 x_{18} & -0.10 x_{34} & -0.09 x_{29} & +  0.03 x_{24} & -1.42 x_{6} & -3.07 x_{11}\\
 x_{12}   &  0.215804729253 & +  0.26 x_{33} & -3.59 x_{13} & -1.33 x_{8} & -2.28 x_{4} & -0.09 x_{26} & -0.01 x_{22} & -0.21 x_{17} & +  1.75 x_{14} & -0.04 x_{31} & +  0.13 x_{18} & -0.20 x_{34} & -0.03 x_{29} & +  0.13 x_{24} & -0.61 x_{6} & -4.37 x_{11}\\
 x_{28}   &  3.5548853789 & +  5.57 x_{33} & -48.61 x_{13} & -18.15 x_{8} & -50.16 x_{4} & -1.87 x_{26} & -0.98 x_{22} & -3.70 x_{17} & + 17.65 x_{14} & -1.55 x_{31} & +  1.98 x_{18} & -3.04 x_{34} & -1.51 x_{29} & +  0.70 x_{24} & -19.75 x_{6} & -78.78 x_{11}\\
 x_{25}   &  1.85363471491 & +  3.78 x_{33} & -23.84 x_{13} & -8.90 x_{8} & -47.10 x_{4} & -1.54 x_{26} & -1.74 x_{22} & -2.39 x_{17} & + 10.77 x_{14} & -1.38 x_{31} & +  0.73 x_{18} & -1.63 x_{34} & -1.37 x_{29} & -0.25 x_{24} & -15.95 x_{6} & -58.91 x_{11}\\
 x_{2}   &  0.190194827538 & +  0.43 x_{33} & -3.81 x_{13} & -0.69 x_{8} & -3.34 x_{4} & -0.17 x_{26} & -0.03 x_{22} & -0.23 x_{17} & +  2.86 x_{14} & -0.08 x_{31} & +  0.14 x_{18} & -0.22 x_{34} & -0.07 x_{29} & +  0.12 x_{24} & -1.22 x_{6} & -6.65 x_{11}\\
 x_{1}   &  0.0723152605954 & -0.40 x_{33} & +  5.87 x_{13} & +  1.83 x_{8} & +  5.04 x_{4} & +  0.14 x_{26} & +  0.03 x_{22} & +  0.32 x_{17} & -3.61 x_{14} & +  0.07 x_{31} & -0.13 x_{18} & +  0.34 x_{34} & +  0.15 x_{29} & -0.21 x_{24} & +  0.75 x_{6} & +  7.16 x_{11}\\
 x_{3}   &  0.23853539451 & +  0.29 x_{33} & -2.73 x_{13} & -0.86 x_{8} & -1.64 x_{4} & -0.09 x_{26} & -0.09 x_{22} & -0.21 x_{17} & +  0.29 x_{14} & -0.04 x_{31} & +  0.09 x_{18} & -0.13 x_{34} & -0.05 x_{29} & +  0.01 x_{24} & -1.04 x_{6} & -4.14 x_{11}\\
 x_{23}   &  0.0573480544981 & +  0.83 x_{33} & +  2.42 x_{13} & -15.10 x_{8} & +  4.86 x_{4} & +  0.34 x_{26} & -0.09 x_{22} & -0.32 x_{17} & -13.96 x_{14} & +  0.01 x_{31} & +  0.48 x_{18} & +  0.33 x_{34} & +  0.34 x_{29} & -0.19 x_{24} & +  4.32 x_{6} & +  6.72 x_{11}\\
 x_{7}   &  0.201807554673 & +  0.67 x_{33} & -7.20 x_{13} & -1.16 x_{8} & -6.75 x_{4} & -0.29 x_{26} & -0.09 x_{22} & -0.43 x_{17} & +  5.14 x_{14} & -0.09 x_{31} & +  0.20 x_{18} & -0.45 x_{34} & -0.17 x_{29} & +  0.23 x_{24} & -1.63 x_{6} & -11.51 x_{11}\\
\hline
z    &  -1.72985018553 & -0.15 x_{33} & -7.46 x_{13} & -5.52 x_{8} & -7.37 x_{4} & -0.17 x_{26} & -0.41 x_{22} & -0.31 x_{17} & +  0.48 x_{14} & -0.32 x_{31} & -0.44 x_{18} & -0.29 x_{34} & -0.34 x_{29} & -0.05 x_{24} & -4.54 x_{6} & -5.90 x_{11}\\
\end{array}\]


 $ x_{14} $ enters and $ x_{23} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{16}   &  11.1657664304 & + 12.65 x_{33} & -84.85 x_{13} & -87.32 x_{8} & -55.22 x_{4} & -2.51 x_{26} & -0.91 x_{22} & -6.96 x_{17} & -4.07 x_{23} & -0.66 x_{31} & +  4.99 x_{18} & -3.58 x_{34} & +  0.01 x_{29} & +  1.57 x_{24} & +  2.70 x_{6} & -123.15 x_{11}\\
 x_{15}   &  0.0875036711156 & +  0.21 x_{33} & -1.91 x_{13} & -2.25 x_{8} & -0.65 x_{4} & -0.01 x_{26} & +  0.04 x_{22} & -0.11 x_{17} & -0.08 x_{23} & +  0.02 x_{31} & +  0.15 x_{18} & -0.11 x_{34} & -0.01 x_{29} & +  0.05 x_{24} & +  0.03 x_{6} & -1.72 x_{11}\\
 x_{9}   &  0.280900505225 & -0.05 x_{33} & +  0.58 x_{13} & +  0.90 x_{8} & +  0.83 x_{4} & -0.01 x_{26} & +  0.05 x_{22} & +  0.04 x_{17} & +  0.02 x_{23} & +  0.06 x_{31} & -0.04 x_{18} & +  0.04 x_{34} & +  0.01 x_{29} & -0.00 x_{24} & +  0.14 x_{6} & +  0.39 x_{11}\\
 x_{19}   &  6.48780410227 & -4.83 x_{33} & + 41.71 x_{13} & + 39.75 x_{8} & + 35.25 x_{4} & +  0.47 x_{26} & +  0.03 x_{22} & +  2.43 x_{17} & +  2.66 x_{23} & +  0.99 x_{31} & -2.70 x_{18} & +  1.93 x_{34} & +  0.35 x_{29} & -2.03 x_{24} & -8.04 x_{6} & + 35.86 x_{11}\\
 x_{32}   &  0.739081318841 & +  8.58 x_{33} & -62.11 x_{13} & -85.29 x_{8} & -19.69 x_{4} & -0.38 x_{26} & -0.89 x_{22} & -4.83 x_{17} & -3.01 x_{23} & -0.73 x_{31} & +  4.20 x_{18} & -2.97 x_{34} & +  0.25 x_{29} & +  1.35 x_{24} & -3.92 x_{6} & -62.98 x_{11}\\
 x_{21}   &  8.22598121604 & +  9.97 x_{33} & -63.34 x_{13} & -78.40 x_{8} & -30.75 x_{4} & -1.30 x_{26} & -0.46 x_{22} & -5.44 x_{17} & -3.35 x_{23} & -0.40 x_{31} & +  4.56 x_{18} & -2.92 x_{34} & -0.10 x_{29} & +  1.33 x_{24} & -9.32 x_{6} & -90.28 x_{11}\\
 x_{30}   &  4.28380046518 & +  6.03 x_{33} & -46.55 x_{13} & -18.42 x_{8} & -11.57 x_{4} & -1.20 x_{26} & -1.28 x_{22} & -3.74 x_{17} & -1.48 x_{23} & -0.46 x_{31} & +  2.02 x_{18} & -1.62 x_{34} & +  0.12 x_{29} & +  0.98 x_{24} & -11.83 x_{6} & -73.65 x_{11}\\
 x_{27}   &  2.88712905185 & +  7.02 x_{33} & -56.43 x_{13} & -43.40 x_{8} & -34.72 x_{4} & -1.38 x_{26} & -1.08 x_{22} & -4.58 x_{17} & -1.97 x_{23} & -0.45 x_{31} & +  2.81 x_{18} & -2.97 x_{34} & -0.14 x_{29} & +  1.18 x_{24} & +  5.37 x_{6} & -66.96 x_{11}\\
 x_{20}   &  5.32512530874 & -7.66 x_{33} & + 47.20 x_{13} & + 76.36 x_{8} & + 33.21 x_{4} & -0.11 x_{26} & +  1.04 x_{22} & +  3.83 x_{17} & +  3.98 x_{23} & +  0.78 x_{31} & -3.08 x_{18} & +  2.42 x_{34} & +  0.09 x_{29} & -1.63 x_{24} & -24.33 x_{6} & + 48.31 x_{11}\\
 x_{10}   &  0.270054101545 & +  0.44 x_{33} & -2.98 x_{13} & -2.75 x_{8} & -1.91 x_{4} & -0.10 x_{26} & -0.08 x_{22} & -0.27 x_{17} & -0.09 x_{23} & -0.06 x_{31} & +  0.13 x_{18} & -0.14 x_{34} & -0.01 x_{29} & -0.00 x_{24} & -0.57 x_{6} & -4.23 x_{11}\\
 x_{5}   &  0.104738836141 & +  0.20 x_{33} & -1.37 x_{13} & -1.20 x_{8} & -1.93 x_{4} & -0.09 x_{26} & -0.02 x_{22} & -0.14 x_{17} & -0.06 x_{23} & -0.04 x_{31} & +  0.07 x_{18} & -0.07 x_{34} & -0.07 x_{29} & +  0.02 x_{24} & -1.15 x_{6} & -2.64 x_{11}\\
 x_{12}   &  0.223003405664 & +  0.36 x_{33} & -3.29 x_{13} & -3.23 x_{8} & -1.67 x_{4} & -0.05 x_{26} & -0.02 x_{22} & -0.25 x_{17} & -0.13 x_{23} & -0.03 x_{31} & +  0.20 x_{18} & -0.15 x_{34} & +  0.01 x_{29} & +  0.11 x_{24} & -0.07 x_{6} & -3.53 x_{11}\\
 x_{28}   &  3.627389065 & +  6.62 x_{33} & -45.55 x_{13} & -37.24 x_{8} & -44.01 x_{4} & -1.45 x_{26} & -1.09 x_{22} & -4.10 x_{17} & -1.26 x_{23} & -1.54 x_{31} & +  2.59 x_{18} & -2.62 x_{34} & -1.07 x_{29} & +  0.45 x_{24} & -14.29 x_{6} & -70.29 x_{11}\\
 x_{25}   &  1.89787270532 & +  4.42 x_{33} & -21.97 x_{13} & -20.55 x_{8} & -43.35 x_{4} & -1.28 x_{26} & -1.81 x_{22} & -2.63 x_{17} & -0.77 x_{23} & -1.37 x_{31} & +  1.10 x_{18} & -1.37 x_{34} & -1.10 x_{29} & -0.40 x_{24} & -12.62 x_{6} & -53.73 x_{11}\\
 x_{2}   &  0.201932138282 & +  0.60 x_{33} & -3.32 x_{13} & -3.78 x_{8} & -2.34 x_{4} & -0.10 x_{26} & -0.05 x_{22} & -0.30 x_{17} & -0.20 x_{23} & -0.07 x_{31} & +  0.24 x_{18} & -0.15 x_{34} & -0.00 x_{29} & +  0.08 x_{24} & -0.34 x_{6} & -5.27 x_{11}\\
 x_{1}   &  0.0575018300708 & -0.62 x_{33} & +  5.24 x_{13} & +  5.73 x_{8} & +  3.79 x_{4} & +  0.05 x_{26} & +  0.05 x_{22} & +  0.40 x_{17} & +  0.26 x_{23} & +  0.07 x_{31} & -0.25 x_{18} & +  0.26 x_{34} & +  0.06 x_{29} & -0.16 x_{24} & -0.37 x_{6} & +  5.43 x_{11}\\
 x_{3}   &  0.239730293916 & +  0.31 x_{33} & -2.68 x_{13} & -1.17 x_{8} & -1.54 x_{4} & -0.08 x_{26} & -0.10 x_{22} & -0.21 x_{17} & -0.02 x_{23} & -0.04 x_{31} & +  0.10 x_{18} & -0.12 x_{34} & -0.05 x_{29} & +  0.01 x_{24} & -0.95 x_{6} & -4.00 x_{11}\\
 x_{14}   &  0.00410711779054 & +  0.06 x_{33} & +  0.17 x_{13} & -1.08 x_{8} & +  0.35 x_{4} & +  0.02 x_{26} & -0.01 x_{22} & -0.02 x_{17} & -0.07 x_{23} & +  0.00 x_{31} & +  0.03 x_{18} & +  0.02 x_{34} & +  0.02 x_{29} & -0.01 x_{24} & +  0.31 x_{6} & +  0.48 x_{11}\\
 x_{7}   &  0.222919114695 & +  0.98 x_{33} & -6.30 x_{13} & -6.72 x_{8} & -4.96 x_{4} & -0.17 x_{26} & -0.12 x_{22} & -0.55 x_{17} & -0.37 x_{23} & -0.09 x_{31} & +  0.37 x_{18} & -0.33 x_{34} & -0.04 x_{29} & +  0.16 x_{24} & -0.04 x_{6} & -9.04 x_{11}\\
\hline
z    &  -1.72789583986 & -0.12 x_{33} & -7.37 x_{13} & -6.04 x_{8} & -7.20 x_{4} & -0.16 x_{26} & -0.41 x_{22} & -0.32 x_{17} & -0.03 x_{23} & -0.32 x_{31} & -0.43 x_{18} & -0.28 x_{34} & -0.33 x_{29} & -0.06 x_{24} & -4.39 x_{6} & -5.67 x_{11}\\
\end{array}\]
Final Dictionary
Solution:  -1.72789583986
Num Pivots:  5
\end{document}
